Analysis of stability law and optimization of slope angle during excavation of deep concave mine slope

Occasional collapse failure is a typical occurrence during mine slope excavation processes. This study aimed to investigate the disaster law in the process of mining slope excavation, and further explore the optimal selection of excavation angle. Based on the systematic analysis of the residual sliding force and deformation response characteristics during slope excavation, the increment of the residual sliding force increases and the stability coefficient decreases with the increase in excavation depth. Additionally, a numerical model of the Jinchuan mining area in Jinchuan City, Gansu Province, China was created using the Midas-GTS finite element software. The influence of different excavation slope angles on slope stability was analyzed via numerical simulation under certain step slope height and width. The results show that the force and deformation of the slope were unfavorable to slope stability, and the slope stability coefficient would decrease gradually with the increase in slope angle. In addition, the optimal excavation angle combination ranges were determined as 62°~ 65°, 64°~ 67°, 67°~ 69°, 70°~ 71°, 73°, 75°~ 76°, 77°~ 80°considering the stability and maximum recovery. Therefore, the above research results verify the loading effect of mine slope excavation, and can serve as a reference for studies on the optimal range of excavation angles for the mine slope.

the submission is accepted. Please make sure it is accurate.   In the process of excavation of slope in deep pit mine, the initial stress equilibrium state 78 in slope body is affected by the excavation behavior and the stress redistribution occurs 79 [20-23]. In fact, the fundamental impact of excavation behavior is to increase the sliding 80 power of the slope, which is equivalent to continuously loading the slope during the 81 whole construction process. At the same time, there will be corresponding displacement 82 near the slope face with the progress of excavation [24][25][26]. It is assumed that the slope 83 of deep concave mine is homogeneous, and the homogeneous body is isotropic, and the 84 thickness of the slope changes uniformly. Taking the potential sliding strip of slope as 85 the research object, the stress of sliding strip under the dynamic action of excavation is 86 as follows (Fig 1). 87 Where Hi1 and Hi1 are respectively the height before and after the excavation of the 88 sliding strip, m; Gi and Gi' are respectively the gravity before and after the excavation Anti-sliding force before excavation： 102 Anti-sliding force after excavation： 103 Therefore, the increment of sliding power of sliding strip caused by excavation is: 112 Only when the slope is excavated downward, the volume of potential sliding soil will 119 increase, and the height of sliding strip will increase. Therefore, it can be considered 120 that the excavation depth corresponds to the remaining sliding force increment in the 121 process of slope excavation in deep depression mine. 122 In the calculation of the slope body, the slope body is assumed to be ideal elastic-123 plastic, and the stress and deformation physical parameters of the slope body section 124 are averaged [27]. According to the basic principle of elastic-plastic mechanics, the 125 relationship between the sliding force and displacement variation caused by the 126 excavation and loading of slope in deep concave mine is expressed as follows.： 127 increase. Therefore, it can be considered that the excavation loading process is the main 136 dynamic factor affecting the sliding dynamic change and displacement change of mine 137 slope. 138

Stability evolution of mine slope under excavation loading condition 139
According to the above formula and the limit equilibrium principle of slope stability, 140 the stability coefficient of mine slope after excavation is determined as follows: 141 Formula 9 shows that only the excavation height variation is the variation parameter 142 in the process of mining slope loading increase, while other physical and geometric 143 parameters are relatively constant. Therefore, the slope stability coefficient is directly 144 related to the dynamic change process of excavation loading. 145

Landslide situation 147
Jinchuan Group quartz open-pit mine is located in Jinchuan District, Jinchang City, 148 Gansu Province, China (Fig 2), and began mining in 1980. The ore area is cut by a 149 series of Sw-Ne strike thrust faults (Fig 3), and the intrusive ore bodies are divided into 150 several sections, which are divided into Ι, Ⅱ, Ⅲ distribution of Jinshan mine is as follows. (Fig 4). Up to now, the mining area has 155 formed a total of 10 steps of 1856m, 1846m, 1836m, 1826m, 1816m, 1792m, 1780m, 156 1768m, 1756m, 1744m and 1732m from top to bottom (Fig 5). With the development 157 of mining, there have been many failures of the slope, such as local landslides on 158 platforms 1816 and 1768 (Fig 6). 159

Numerical simulation 160
According to the actual situation of the mining area, the section 5C~1C of the north 161 slope of the mining area where local landslide occurred was selected as the modeling 162 object, including 7 steps (between 1826m and 1732m) (Fig 7). 163 According to the geological survey and test data provided by the mining area, the 164 physical and mechanical parameters of the rock mass in the mining area are as follows 165 ( According to the selected research object, four kinds of excavation slope Angle 168 parameters are set in the experimental scheme. The excavation Angle increases 169 gradually in schemes 1 to 2, and the overall steepening of multi-step slope in schemes 170 3 to 4 (Table 2). Before the numerical simulation of the experimental scheme, the design 171 scheme of the mine slope is simulated first, which is convenient for comparative 172 analysis. 173 Midas~GTS software was used to calculate the overall stability coefficient of slope 175 respectively for the design scheme and the experimental scheme. According to the 176 calculation results, the stress change, displacement change, plastic zone distribution and 177 overall stability coefficient after excavation were compared and analyzed. By referring 178 to the relevant specifications, the limit value of slope stability coefficient is determined 179 as 1.3, and the stability coefficient of each scheme was compared with the specification 180 value. 181

Results analysis
182

Stress field analysis 184
The stress cloud diagram during slope excavation is shown below. Before the 185 excavation, the horizontal stress of the slope is all compressive stress, and the stress 186 field is uniform strip distribution. When the slope is excavated to 1732 platform, the 187 horizontal stress of the slope body is compressive stress, which increases with the 188 increase of slope depth. Stress concentration occurs at the foot of each step slope, and 189 the stress in other parts is basically distributed in a uniform band (Fig 8). Similar to the 190 distribution of horizontal stress field, the excavation also destroys the vertical initial 191 stress state of the slope and causes the stress redistribution of the slope. The vertical 192 stress of the slope is also compressive stress, but there is no stress concentration. (Fig  193   9). Therefore, the vertical stress has little damage to the slope. 194 Considering that the horizontal stress has a great influence on the slope, the element 195 located in the middle of each step and the top of the slope is selected in the model, and 196 its horizontal stress value is extracted. Thus, the curve of horizontal stress variation of 197 each step during slope excavation is drawn (Fig 10). It can be seen from the figure  198 that with the progress of excavation, the horizontal stress of the slope and the top has 199 the same change trend, and the horizontal compressive stress of the lower step gradually 200 decreases, with a decrease of about 50%. At the same time, the horizontal compressive 201 stress of the first and second steps is also in a stable state without increasing trend. In 202 addition, for the same step, the value of horizontal compressive stress at the top of the 203 slope is less than that at the middle of the slope, which is caused by the fact that tensile 204 failure usually appears at the top of the slope first. In addition, because each step is in 205 the "underground" state first, and then excavated to form a part of the slope. Therefore, 206 the change in the early stage of the curve in Figure 8 shows an irregular "rise and fall" 207 phenomenon, and the change trend is consistent after excavation. 208 The element located in the middle of each step is selected in the model, and the 216 horizontal displacement value is extracted to make the curve of the horizontal 217 displacement of each step in the process of slope excavation (Fig 12). As can be seen 218 from the figure, the step at the upper part of the slope has a negative displacement, and 219 the displacement gradually increases and tends to be stable. The step at the lower part 220 of the slope has a positive displacement, and the displacement value increases gradually. 221

Displacement field analysis
If the excavation continues downward, it can be predicted that when the negative 222 displacement of the upper step of the slope tends to be stable, its value will gradually 223 develop to the positive displacement, while the positive displacement of the lower step 224 will continue to increase. 225

Plastic zone and the global stability analysis 226
According to the distribution range of plastic zones, plastic zones are generated from 227 the foot of each step slope, and then start to develop upward, and gradually connect and 228 penetrate (Fig 13). The stability coefficient of slope during excavation can be obtained 229 by strength reduction method (Fig 14). Fig 14 shows that the stability coefficient 230 decreases with the excavation of the slope. At the fourth step of excavation, the stability 231 coefficient rises, which is caused by the redistribution of the slope stress during the 232 dynamic excavation. The cracks or shear failure caused by the previous excavation will 233 close with the redistribution of stress, resulting in the new stability of rock and soil 234 weight；It can also be seen from the cloud map of plastic zone that during the fourth 235 excavation step, the range of plastic zone generated by the third and fourth steps is very 236 small compared with other parts. This also indicates that when the slope is excavated 237 to the fourth layer, its stability coefficient is larger than that of the first three steps. But 238 in general, with the progress of excavation, the stability of slope gradually decreases 239 until the end of mining. 240 The element located in the middle and foot of each step is selected in the model, and 241 its maximum shear stress value is extracted, and the maximum shear stress curve of 242 each step in the process of slope excavation is made. Fig15 shows that with the progress 243 of excavation, the variation trend of maximum shear stress at the middle and foot of 244 slope is basically the same. The shear stress of the first and second steps is relatively 245 stable, while the shear stress of the other steps decreases before excavation. However, 246 after excavation, the shear stress begins to increase and gradually tends to be stable. In 247 addition, for the same step, the shear stress at the foot of the slope is greater than that 248 at the middle of the slope, which is caused by the shear failure usually appearing at the 249 foot of the slope first. It is worth noting that the shear stress curves in the early stage all 250 show a downward trend, which is due to the fact that each step is "underground". 251 However, after the excavation, the shear stress variation trend of each step is basically 252 the same. 253

Analysis of experimental scheme 254
According to the simulation results of schemes 1~2, the distribution rules of horizontal 255 stress, horizontal displacement and vertical stress and vertical displacement are 256 basically similar to those of the design scheme. Among them, the horizontal 257 displacement in schemes 1 to 2 changes with the change of slope Angle, the negative 258 horizontal displacement gradually decreases, and the positive horizontal displacement 259 gradually increases (Tables 3 and 4). This range gradually expands from the bottom of 260 the slope to the top of the slope. The vertical displacement decreases gradually with the 261 increase of slope Angle, that is, the recovery value of excavation unloading of rock 262 mass decreases, but the reduction range is limited. 263 Table 3  The distribution of plastic zone in schemes 1~2 is different from that in the design 264 scheme: with the increase of slope Angle, the plastic zone at the foot of the slope of 265 steps 3~4 is gradually reduced compared with that in the design scheme, while the 266 plastic zone at steps 5~7 is gradually increased compared with that in the design scheme. 267 Therefore, there is a greater risk of local landslide at steps 5 to 7, which needs to be 268 controlled during construction (Fig 16). 269 According to the simulation results of schemes 3-4, the distribution rules of 270 horizontal displacement, vertical displacement and vertical stress of slope are consistent 271 with those of the schemes mentioned above. However, the distribution of horizontal 272 tensile stress in schemes 3-4 gradually moves to the upper part of the slope. With the 273 change of slope Angle in scheme 3 and 4, the plastic zone at the foot of slope of step 3 274 and 4 continues to decrease, and the plastic zone at the foot of slope of step 5 to 7 275 continues to expand to the top of slope, while the plastic zone at the foot of slope of 276 step 1 and 2 is gradually connected. 277 As shown in Table 5 and Fig 17, the slope stability coefficient gradually decreases 279 with the increase of slope excavation depth and slope Angle. When the first five steps 280 are excavated, the stability coefficients of schemes 1 to 2 are all greater than 1.3, and 281 the reduction of stability coefficients of the last two steps is also limited after the 282 excavation is completed. Considering the control of the maximum mining amount and 283 the calculation results of the strength reduction method in Midas GTS finite element 284 software tend to be safe, the slope Angle of scheme 2 can be considered as the limit 285 range temporarily. With the increase of the overall slope Angle in scheme 3 and 4, the 286 stability coefficient also shows a trend of gradual decrease. However, the final safety 287 coefficient of scheme 3 and 4 decreases to around 1.3, and the stability coefficient of 288 scheme 4 is lower than 1.3, so it is not considered. Considering that the stability 289 coefficient obtained by Midas GTS finite element software tends to be safe and 290 combined with the above mentioned, the combination range of the optimal slope step 291 slope Angle is finally determined to be between scheme 2 and scheme 3. 292

293
Under the condition of excavation loading, this paper analyzes the sliding force, 294 deformation response and stability change of slope in deep pit mine, carries out 295 numerical simulation of slope mining in open pit deep pit mine in Jinchang, Gansu 296 Province, China, and draws the following conclusions: 297 (1)The excavation loading process of mine slope is a one-way process of reducing 298 stability. The loading effect of this kind of slope is shown as the increase of sliding 299 power and deformation response. The variation of sliding force is mainly affected by 300 the excavation height, slope inclination Angle and physical and mechanical properties 301 of slope body. Among them, the change of excavation height is the main dynamic factor 302 leading to the increase of sliding force of mine slope, which indicates that the process 303 of excavation loading is a subjective factor affecting the stability of this kind of slope. 304 (2)With the progressive mining of open-pit multi-stage slope, both the horizontal 305 stress and the vertical stress increase gradually, and the stress concentration at the foot 306 of slope mainly depends on the horizontal stress; The horizontal displacement gradually 307 changed from negative to positive, and the uplift of slope and pit bottom also increased 308 gradually; The plastic zone appeared at the foot of step slope and gradually expanded 309 upward. The overall stability coefficient of slope shows a downward trend. 310 (3)With the increase of slope Angle, the stability coefficient of slope decreases 311 gradually under the four experimental schemes. A small recovery in the safety factor in 312 individual scenarios is caused by stress redistribution and the re-closure of existing 313 fractures or shear bands. 314 (4)According to the results of design scheme and experiment scheme, the optimal 315 value range of slope Angle of each step is finally determined between scheme 2 and 316 Scheme 3. That is 62°~ 65°、64°~ 67°、67°~ 69°、70°~ 71°、73°、75°~ 76°、77°~ 317 80°. 318